Acoustic resonators are used to filter electrical signals in various electronic applications. For example, acoustic resonators are used as bandpass filters in cellular phones, global positioning system (GPS) devices, and imaging applications, to name but a few.
An acoustic resonator can be characterized generally by a center frequency and bandwidth. However, due to a variety of intrinsic and extrinsic influences, the center frequency and bandwidth can drift over time, which may be referred to as frequency drift, or more generally “aging.” One cause of aging in acoustic resonators is physical stress, specifically a differential stress. A differential stress refers to the membrane being forced to bow, buckle or be stretched (like a Kettle Drum) in response to differential forces applied to the different edges of the resonator. The source of this differential stress, that is the physical stress, can be caused, for example, by forces transmitted to the acoustic resonator through adjacent components.
Notably, the acoustic resonator is inside a small package; typically a chip-scale package. In many cases, the chip-scale package may be an all-silicon MEMs like package. As an example, an acoustic resonator (in an all-silicon package) can be mounted on a printed circuit board (PCB) comprising metal and laminate components. As the PCB is heated or cooled, the PCB may expand or contract unevenly because the metal and laminate components have different temperature coefficients of expansion. This uneven expansion or contraction can cause the PCB to change shape in a “potato chip” fashion. As the PCB changes shape, the PCB will transfer forces to the acoustic resonator through various intervening components, such as an epoxy bonding material, or the silicon package containing the acoustic resonator. As these forces are transferred to the acoustic resonator, they will change the center frequency of the acoustic resonator. Although the frequency change is relatively small, it is significant in terms of other sources of aging such as the electrode metal relaxation effect associated with quartz crystal aging.
FIG. 1A is a diagram illustrating an acoustic resonator inside of an all-silicon, chip-scale package mounted on a PCB using a standard epoxy, and FIG. 1B is a diagram illustrating forces applied to the acoustic resonator. For example, it may be assumed that acoustic resonator 115 is located inside a chip-scale package 100 mounted on a PCB 101. Forces are applied to the chip-scale package 100 from the PCB 101, and from the chip-scale package 100 to acoustic resonator structure as indicated by arrows in FIG. 1B. The forces shown in FIG. 1B can originate from various sources. For example, forces can originate from the PCB 101 when it has been warped in response to temperature changes, as described above. Alternatively, forces could originate from the PCB 101 that has been bent when clamped to a chassis or another motherboard, or from the soldering of the chip-scale package 100 package onto the PCB 101.
More particularly, referring to FIGS. 1A and 1B, the chip-scale package 100 comprises a silicon substrate 105 with an acoustic resonator mounted inside (which may be a film bulk acoustic resonator (FBAR) or a contour mode acoustic resonator, or a Rayliegh-Lamb mode type resonator, for example) and a silicon lid (or microcap structure) 106. The lid 106 is attached to the substrate 105 by a sealant or gasket 123, for example. An air gap 110 is formed between substrate 105 and acoustic resonator 115 so that acoustic resonator 115 can resonate freely.
Curved lines 120 represent the interface of the mounted resonator shown with other structures, such as the PCB 101, the chip-scale packaging, etc. Forces created by, or presented to these structures can be present. These forces can be transferred from the package to substrate 105 through various intervening features, such as an epoxy bonding 122 or lid 106. The transferred forces create stresses 125 on substrate 105. Stresses 125 propagate through substrate 105 and other features to create stresses 130 where acoustic resonator 115 is connected to substrate 105. Stresses 130 exert torque on acoustic resonator 115, which can change the center frequency on the acoustic resonator 115.
FIG. 1C is a diagram illustrating a simulation of forces transferred from substrate 105 to acoustic resonator 115. As illustrated in FIG. 1C, the forces on substrate 105 cause stress at an edge of acoustic resonator 115. The stress is transmitted horizontally through acoustic resonator 115, which can affect the resonance of the acoustic resonator 115, as explained above.
FIG. 2A is a graph illustrating changes of the center frequency of a conventional acoustic resonator structure as a function of temperature, where the device temperature is swept from about 20° C. to about 130° C. several times. The parabolic nature of the frequency dependence on temperature is an intrinsic property of a so-called zero drift resonator (ZDR). However, the apparent hysteresis—or shift from one temperature run to the next—is due to the externally applied stresses. The graph of FIG. 2A was generated with the ZDR mounted on a PCB in laboratory conditions. A resonator under real-life conditions may experience even more frequency “hysteresis” than that illustrated in FIG. 2A.
Referring to FIG. 2A, the ZDR was heated from an initial temperature of approximately 70° C. to a temperature of approximately 130° C. The resonator was then cooled to approximately 25° C. and heated back to approximately 70° C. The center frequency of the acoustic resonator changed by approximately −50 ppm when the temperature was raised from 70° C. to 130° C. Then, as the temperature was cooled back to 70° C., the center frequency passed through a point at 0 ppm, which is offset from the original center frequency by approximately 20 ppm. As illustrated by the different center frequencies exhibited at 70° C., the center frequency of the acoustic resonator exhibits both temperature dependence as well as temperature based hysteresis. The parabolic temperature dependence is a property of the stiffness of the materials present in the acoustic stack of the ZDR and can be compensated elsewhere in the circuit. But, the hysteresis is created by variations in applied forces to the substrate. One cause for the change in force is that the epoxy (a hydrophilic material) outgases moisture and as the epoxy becomes more desiccated, it shrinks and thus applies a different force to the mounted ZDR. The use of softer epoxies helps mitigate, but not eliminate, the transfer of stress from the PCB to the acoustic resonator.
Not shown, but we have measured, is that when one also does injection molding to cover the die (as typical of today's ASIC chips in QFN packages), the transfer of stress is magnified and, if the customer does the injection molding, there is no hope of controlling the amount of offset in frequency created by the applied physical stresses.
The frequency changes shown in FIG. 2A will be too large for many high accuracy electronic applications. For example, GPS devices can only tolerate aging-related frequency changes on the order of +/−0.5 ppm. Similarly, wireless applications, such as low power radios used in WiFi or Bluetooth can only tolerate aging-related frequency changes on the order of +/−10 ppm.
Acoustic resonators have an associated turnover temperature (TOT), which is the temperature at which the center frequency does not change with temperature. FIG. 2B is a graph illustrating TOT curves for two different acoustic resonators, one having an AlN piezoelectric layer with a thickness of 29,530 Å and electrodes with a thickness of 2,800 Å (solid line), and another having an AlN piezoelectric layer with a thickness of 29,100 Å and electrodes with a thickness of 2,900 Å (dotted line). At TOT, changes in frequency versus changes in temperature are quite small. Therefore, when the temperature of the acoustic resonator is kept close to the TOT (e.g., within about 1° C.), then changes in frequency of the acoustic resonator due to any (ambient) temperature variations will be very small. For example, at TOT, the second order coefficient of temperature β of a typical ZDR stack is −20 ppb/C2. Thus, even a maximum 1° C. temperature excursion would incur only a 0.02 ppm frequency shift. In comparison, the second order coefficient of temperature β of a ZDR stack according to representative embodiments is only −10 ppb/C2. This means that if the temperature (or the TOT) is off by +/−10° C., the error in stability is only+/−1 ppm.
What is needed, therefore, are techniques for reducing frequency drift due to physical stresses in acoustic resonator structures, including changes in temperature.